While it is widely acknowledged that forest biodiversity contributes to climate change mitigation through improved carbon sequestration, conversely how climate affects tree species diversity - forest productivity relationships is still poorly understood. We combined the results of long-term experiments where forest mixtures and corresponding monocultures were compared on the same site to estimate the yield of mixed-species stands at a global scale, and its response to climatic factors. We found positive mixture effects on productivity using a meta-analysis of 126 cases studies established at 60 sites spread across five continents. Overall, the productivity of mixed-species forests was 15% greater than the average of their component monocultures, and not statistically lower than productivity of the best component monoculture. Productivity gains in mixed-species stands were not affected by tree age or stand species composition but significantly increased with local precipitation. The results should guide better use of tree species combinations in managed forests and suggest that increased drought severity under climate change might reduce the atmospheric carbon sequestration capacity of natural forests.